Is there a non-channeling orientation?

Author(s):  
J. A. Eades ◽  
K. K. Christenson ◽  
M. L. Andreessen

In the standard form of ALCHEMI, the aim is to calculate the fraction of an impurity that is substitutional on each different sublattice of the host crystal. The result is calculated from the ratios of the of the intensities of the x rays emitted by the elements present. The ratios vary as a function of the angle of the incident electron beam because of electron channeling in the crystal structure. The channeling has the effect of making the electron density different in different parts of the unit cell. If the x-ray yield of one element goes up, the electron yield of any other element on the same sites (i.e. the same sublattice) in the crystal structure will go up in the same proportion. This variation can be used to calculate the fraction on each site.The calculation requires the measurement of the x-ray ratios at at least one angle with a strong channeling effect but also requires the measurement of the ratios at a condition of the incident beam that is “nonchanneling”, that is when the electron flux is uniform across the unit cell.

The present paper deals with the results obtained in the investigation of the atomic structure of rutile and cassiterite by the X-ray spectrometer. A detailed account of the method has been given by Prof. Bragg and his son, W. L. Bragg, in a series of papers communicated to the Royal Society. It consists essentially in allowing a narrow beam of monochromatic X-rays—in this case the rhodium rays—to fall on the face of the crystals, mounted on a spectrometer table, the axis of rotation of which passes through the face of the crystal. The beam is “reflected” by the atom planes parallel to this face, and thence passes into an ionisation chamber, containing methyl bromide in order to increase the ionisation current. The setting of crystal and chamber with regard to the incident beam corresponds to that for which ordinary light is reflected.


Since the appearance of Sir William Bragg’s first work on the structure of martz (these ‘Proceedings,’ A, vol. 89, p. 595 (1914)) this mineral has been the subject of many investigations. It has lent itself very well to study by the older crystallographic methods, by which, from symmetry considerations, has been placed in the trapezohedral class of the trigonal system, i. e ., it exhibits trigonal symmetry about one ( c ) axis and digonal symmetry about ree others, lying symmetrically in a plane perpendicular to the first and intersecting in it. Two enantiomorphous forms were found to exist. Investigation by the X-ray spectrometer method enabled Bragg to give the dimensions of the unit triangular prismatic cell as a = 4·89 Å. U. and = 5·375 Å. U., whilst density considerations clearly indicated that three olecules were associated with such a unit cell. It was also shown that the three molecules were associated with the unit cell in such a way that planes of equal weight occurred at o , c /3, 2 c /3, c , etc., along the vertical c axis.


The quartz crystal has a trigonal axis and three digonal axes, which are at right angles to the trigonal axis. It has no other element of symmetry. It belongs to Class 18 of the 32 classes into which crystals may be divided by their outside appearance. It was shown in 1913, by the methods of X-ray analysis, which were then new, that the unit cell contains three molecules of SiO 2 , which are so arranged that a revolution of 120° round the principal axis, coupled with a translation c /3 along it, brings each molecule into the exact position previously occupied by one of its companions. The trigonal axis is in fact a screw axis. The value of c is 5·375 A. U. The distance between an axis and each of its six equidistant neighbours is 4·89 A. U. Each silicon molecule possesses a digonal axis. This particular arrangement of molecules is known in mathematical crystallography as that of the space-group D 4 3 or D 6 3 , according to the rotatory sense of the lattice. At this stage of the work four parameters, still remained to be determined before the positions of the atoms in the crystal structure could be defined. The position will be clear from a consideration of fig. 1, which is reproduced from ‘X-rays and Crystal Structure,’ p. 261. Each of the two diagrams in the figure shows the relation between three molecules, forming the content of the unit cell, and derivable from each other in the manner described. In one, the screw axis is in the plane of the paper, in the other at right angles to it. The digonal axes are also shown. The distance of the silicon (black disc) from the axis is one of the unknowns: the spatial relations of the oxygens to the silicons require for their definition three more. The diagram of fig. 2 shows various possible positions of the silicon atoms when projected upon the basal plane. They must lie on certain lines, as shown, in order to satisfy the symmetry conditions.


Author(s):  
David C. Joy

In a crystalline solid the regular arrangement of the lattice structure influences the interaction of the incident beam with the specimen, leading to changes in both the transmitted and backscattered signals when the angle of incidence of the beam to the specimen is changed. For the simplest case the electron flux inside the specimen can be visualized as the sum of two, standing wave distributions of electrons (Fig. 1). Bloch wave 1 is concentrated mainly between the atom rows and so only interacts weakly with them. It is therefore transmitted well and backscattered weakly. Bloch wave 2 is concentrated on the line of atom centers and is therefore transmitted poorly and backscattered strongly. The ratio of the excitation of wave 1 to wave 2 varies with the angle between the incident beam and the crystal structure.


Minerals ◽  
2020 ◽  
Vol 10 (11) ◽  
pp. 1028 ◽  
Author(s):  
M. Mashrur Zaman ◽  
Sytle M. Antao

This study investigates the crystal chemistry of monazite (APO4, where A = Lanthanides = Ln, as well as Y, Th, U, Ca, and Pb) based on four samples from different localities using single-crystal X-ray diffraction and electron-probe microanalysis. The crystal structure of all four samples are well refined, as indicated by their refinement statistics. Relatively large unit-cell parameters (a = 6.7640(5), b = 6.9850(4), c = 6.4500(3) Å, β = 103.584(2)°, and V = 296.22(3) Å3) are obtained for a detrital monazite-Ce from Cox’s Bazar, Bangladesh. Sm-rich monazite from Gunnison County, Colorado, USA, has smaller unit-cell parameters (a = 6.7010(4), b = 6.9080(4), c = 6.4300(4) Å, β = 103.817(3)°, and V = 289.04(3) Å3). The a, b, and c unit-cell parameters vary linearly with the unit-cell volume, V. The change in the a parameter is large (0.2 Å) and is related to the type of cations occupying the A site. The average <A-O> distances vary linearly with V, whereas the average <P-O> distances are nearly constant because the PO4 group is a rigid tetrahedron.


Author(s):  
Matthew Wilding ◽  
Colin Scott ◽  
Thomas S. Peat ◽  
Janet Newman

The NAD-dependent malonate-semialdehyde dehydrogenase KES23460 fromPseudomonassp. strain AAC makes up half of a bicistronic operon responsible for β-alanine catabolism to produce acetyl-CoA. The KES23460 protein has been heterologously expressed, purified and used to generate crystals suitable for X-ray diffraction studies. The crystals belonged to space groupP212121and diffracted X-rays to beyond 3 Å resolution using the microfocus beamline of the Australian Synchrotron. The structure was solved using molecular replacement, with a monomer from PDB entry 4zz7 as the search model.


Minerals ◽  
2018 ◽  
Vol 8 (8) ◽  
pp. 311 ◽  
Author(s):  
Carlotta Giacobbe ◽  
Jonathan Wright ◽  
Dario Di Giuseppe ◽  
Alessandro Zoboli ◽  
Mauro Zapparoli ◽  
...  

Nowadays, due to the adverse health effects associated with exposure to asbestos, its removal and thermal inertization has become one of the most promising ways for reducing waste risk management. Despite all the advances in structure analysis of fibers and characterization, some problems still remain that are very hard to solve. One challenge is the structure analysis of natural micro- and nano-crystalline samples, which do not form crystals large enough for single-crystal X-ray diffraction (SC-XRD), and their analysis is often hampered by reflection overlap and the coexistence of multiple fibres linked together. In this paper, we have used nano-focused synchrotron X-rays to refine the crystal structure of a micrometric tremolite fibres from Val d’Ala, Turin (Italy) after various heat treatment. The structure of the original fibre and after heating to 800 °C show minor differences, while the fibre that was heated at 1000 °C is recrystallized into pyroxene phases and cristobalite.


1985 ◽  
Vol 40 (6) ◽  
pp. 726-729 ◽  
Author(s):  
Klaus Güde ◽  
Christoph Hebecker

Abstract Single crystals of KSc2F7 have been prepared from a mixture of KF and ScF3 . The samples were investigated by X-ray methods. KSc2F7 crystallizes orthorhombically with a = 10.643(2), b = 6.540(1), c = 4.030(1) Å. These data indicate a close crystallographic connection to the monoclinic unit cell of KIn2F7 [1], But in contrast to KIn2F7 , KSc2 F7 crystallizes in space group No. 65. Cmmm - D192h. The R-value for 341 observed independent reflections is 0.060.


1983 ◽  
Vol 38 (5) ◽  
pp. 554-558 ◽  
Author(s):  
Herbert Binder ◽  
Walter Matheis ◽  
Hans-Jörg Deiseroth ◽  
Han Fu-Son

Abstract Acyloxyfluoroboranes Trimeric alkoxydifluoroboranes (F2BOR)3 (2) react with organic acid anhydrides by substitution of a ring group OR forming monocyclic acyloxyfluoroboranes of the type 2,2,6,6-tetrafluoro-l,4-dialkyl-l,3,5-trioxa-2,6-diboracyclohexene (3). The X-ray crystal structure determination of 3a shows two conformational isomers: two planar and two non-planar six-membered rings are present in the unit cell. The ring conformation is influenced by weak intermolecular H — F interactions.


1985 ◽  
Vol 40 (1) ◽  
pp. 13-18 ◽  
Author(s):  
Kay Jansen ◽  
Kurt Dehnicke ◽  
Dieter Fenske

The syntheses and IR spectra of the complexes [Mo2(O2C-Ph)4X2]2⊖ with X = N3, CI, Br and the counter ion PPh4⊕ are reported. The azido and the bromo complexes are obtained from a solution of [Mo2(O2CPh)4] with PPh4N3 in pyridine or by reaction with PPh4Br in CH2Br2, respectively. When (PPh4)2[Mo2(O2CPh)4(N3)2] is dissolved in CH2Cl2, nitrogen is evolved and the complex with X = CI is obtained. The crystal structure of (PPh4)2[Mo2(O2CPh)4Cl2] · 2CH2Cl2 was determined from X-ray diffraction data (5676 observed independent reflexions, R = 0.042). It crystallizes in the monoclinic space group P21/n with four formula units per unit cell; the lattice constants are a = 1549, b = 1400, c = 1648 pm, β = 94.6°. The centrosymmetric [Mo2(O2CPh)4Cl2]2⊖ ion has a rather short Mo-Mo bond of 213 pm, whereas the MoCl bonds are very long (288 pm)


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